Systems and methods for estimating ischemia and blood flow characteristics from vessel geometry and physiology

ABSTRACT

Systems and methods are disclosed for determining individual-specific blood flow characteristics. One method includes acquiring, for each of a plurality of individuals, individual-specific anatomic data and blood flow characteristics of at least part of the individual&#39;s vascular system; executing a machine learning algorithm on the individual-specific anatomic data and blood flow characteristics for each of the plurality of individuals; relating, based on the executed machine learning algorithm, each individual&#39;s individual-specific anatomic data to functional estimates of blood flow characteristics; acquiring, for an individual and individual-specific anatomic data of at least part of the individual&#39;s vascular system; and for at least one point in the individual&#39;s individual-specific anatomic data, determining a blood flow characteristic of the individual, using relations from the step of relating individual-specific anatomic data to functional estimates of blood flow characteristics.

RELATED APPLICATION

This application claims priority to U.S. Provisional Application No.61/700,213 filed Sep. 12, 2012, and 61/793,673, filed Mar. 15, 2013, theentire disclosures of which are hereby incorporated by reference intheir entireties.

FIELD OF THE INVENTION

Various embodiments of the present disclosure relate generally tomedical imaging and related methods. More specifically, particularembodiments of the present disclosure relate to systems and methods forestimating patient-specific blood flow characteristics from vesselgeometry and physiology.

In addition, embodiments of the present disclosure relate to rapidestimation of ischemia, blood flow, fractional flow reserve (FFR), orother metrics derived from patient-specific anatomy and characteristicsto aid physicians in the diagnosis, management, and treatment ofcardiovascular diseases.

BACKGROUND

Cardiovascular diseases are the leading cause of death in theindustrialized world and contribute to roughly a third of global deaths.The predominant form of acquired cardiovascular disease,atherosclerosis, results from the chronic buildup of fatty material inthe inner layer of the arteries supplying the heart, brain, kidneys,digestive system, and lower extremities. Progressive coronary arterydisease restricts blood flow to the heart, presenting as chest painduring physical exertion, referred to as chronic stable angina, or whenthe patient is at rest, known as unstable angina. More severemanifestation of disease may lead to myocardial infarction, or heartattack. Patients presenting with chest pain are usually subject to arange of currently available noninvasive tests, including ECG, treadmilltests, SPECT, PET, and CT—none of which measure blood flow and provideonly anatomic information or indirect indications of disease. Due to thelack of accurate functional information provided by current noninvasivetests, many patients require invasive catheter procedures to assesscoronary blood flow. There is a pressing need for a noninvasive means toquantify blood flow in the human coronary arteries to assess thefunctional significance of diffuse and focal coronary artery disease.Additionally, there is a need to achieve rapid assessment of blood flowto enable use in emergency rooms, in-patient treatment, and onsitehospital use. In addition to non-invasive use, there is a need withininvasive imaging, such as coronary angiography, to quickly estimatefunctional metrics without the need for pressure or flow wires orspecial medication. Such a technology is also applicable to preventing,diagnosing, managing and treating disease in other portions of thecardiovascular system including the arteries of the neck, e.g. thecarotid arteries, the arteries in the head, e.g. the cerebral arteries,the arteries in the abdomen, e.g. the abdominal aorta and its branches,the arteries in legs, e.g. the femoral and popliteal arteries.

A functional assessment of arterial capacity is important for treatmentplanning to address patient needs. Recent studies have demonstrated thathemodynamic characteristics, such as Fractional Flow Reserve (FFR), areimportant indicators to determine the optimal treatment for a patientwith arterial disease. Conventional assessments of these hemodynamiccharacteristics use invasive catheterizations to directly measure bloodflow characteristics, such as pressure and flow velocity. However,despite the important clinical information that is gathered, theseinvasive measurement techniques present severe risks to the patient andsignificant costs to the healthcare system.

To address the risks and costs associated with invasive measurement, anew generation of noninvasive tests have been developed to assess bloodflow characteristics. These noninvasive tests use patient imaging (suchas computed tomography (CT)) to determine a patient-specific geometricmodel of the blood vessels and this model is used computationally tosimulate the blood flow using computational fluid dynamics (CFD) withappropriate physiological boundary conditions and parameters. Examplesof inputs to these patient-specific boundary conditions include thepatient's blood pressure, blood viscosity and the expected demand ofblood from the supplied tissue (derived from scaling laws and a massestimation of the supplied tissue from the patient imaging). Althoughthese simulation-based estimations of blood flow characteristics havedemonstrated a level of fidelity comparable to direct (invasive)measurements of the same quantity of interest, physical simulationsdemand a substantial computational burden that can make these virtual,noninvasive tests difficult to execute in a real-time clinicalenvironment. Consequently, the present disclosure describes newapproaches for performing rapid, noninvasive estimations of blood flowcharacteristics that are computationally inexpensive.

SUMMARY

Systems and methods are disclosed for deriving a patient-specificgeometric model of a patient's blood vessels, and combining thisgeometry with the patient-specific physiological information andboundary conditions. Combined, these data may be used to estimate thepatient's blood flow characteristics and predict clinically relevantquantities of interest (e.g., FFR). The presently disclosed systems andmethods offer advantages over physics-based simulation of blood flow tocompute the quantity of interest, such as by instead using machinelearning to predict the results of a physics-based simulation. In oneembodiment, disclosed systems and methods involve two phases: first, atraining phase in which a machine learning system is trained to predictone or more blood flow characteristics; and second, a production phasein which the machine learning system is used to produce one or moreblood flow characteristics and clinically relevant quantities ofinterest. In the case of predicting multiple blood flow characteristics,this machine learning system can be applied for each blood flowcharacteristic and quantity of interest.

According to one embodiment, a method is disclosed for determiningindividual-specific blood flow characteristics. The method includesacquiring, for each of a plurality of individuals, individual-specificanatomic data and blood flow characteristics of at least part of theindividual's vascular system; executing a machine learning algorithm onthe individual-specific anatomic data and blood flow characteristics foreach of the plurality of individuals; relating, based on the executedmachine learning algorithm, each individual's individual-specificanatomic data to functional estimates of blood flow characteristics;acquiring, for an individual, individual-specific anatomic data of atleast part of the individual's vascular system; and for at least onepoint in the individual's individual-specific anatomic data, determininga blood flow characteristic of the individual, using relations from thestep of relating individual-specific anatomic data to functionalestimates of blood flow characteristics.

According to one embodiment, a system is disclosed for determiningindividual-specific blood flow characteristics. The system includes adata storage device storing instructions for estimatingindividual-specific blood flow characteristics; and a processorconfigured to execute the instructions to perform a method including thesteps of: acquiring, for each of a plurality of individuals,individual-specific anatomic data and blood flow characteristics of atleast part of the individual's vascular system; executing a machinelearning algorithm on the individual-specific anatomic data and bloodflow characteristics for each of the plurality of individuals; relating,based on the executed machine learning algorithm, each individual'sindividual-specific anatomic data to functional estimates of blood flowcharacteristics; acquiring, for an individual, individual-specificanatomic data of at least part of the individual's vascular system; andfor at least one point in the individual's individual-specific anatomicdata, determining a blood flow characteristic of the individual, usingrelations from the step of relating individual-specific anatomic data tofunctional estimates of blood flow characteristics.

According to one embodiment, a non-transitory computer-readable mediumstoring instructions that, when executed by a computer, cause thecomputer to perform a method including: acquiring, for each of aplurality of individuals, individual-specific anatomic data and bloodflow characteristics of at least part of the individual's vascularsystem; executing a machine learning algorithm on theindividual-specific anatomic data and blood flow characteristics foreach of the plurality of individuals; relating, based on the executedmachine learning algorithm, each individual's individual-specificanatomic data to functional estimates of blood flow characteristics;acquiring, for an individual, individual-specific anatomic data of atleast part of the individual's vascular system; and for at least onepoint in the individual's individual-specific anatomic data, determininga blood flow characteristic of the individual, using relations from thestep of relating individual-specific anatomic data to functionalestimates of blood flow characteristics.

Additional objects and advantages of the disclosed embodiments will beset forth in part in the description that follows, and in part will beapparent from the description, or may be learned by practice of thedisclosed embodiments. The objects and advantages of the disclosedembodiments will be realized and attained by means of the elements andcombinations particularly pointed out in the appended claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory onlyand are not restrictive of the disclosed embodiments, as claimed.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are incorporated in and constitute apart of this specification, illustrate various exemplary embodiments andtogether with the description, serve to explain the principles of thedisclosed embodiments.

FIG. 1 is a block diagram of an exemplary system and network forestimating patient-specific blood flow characteristics from vesselgeometry and physiological information, according to an exemplaryembodiment of the present disclosure.

FIG. 2 is a block diagram of an exemplary method for estimatingpatient-specific blood flow characteristics from vessel geometry andphysiological information, according to an exemplary embodiment of thepresent disclosure.

DESCRIPTION OF THE EMBODIMENTS

Reference will now be made in detail to the exemplary embodiments of thedisclosure, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

The present disclosure describes certain principles and embodiments forproviding advantages over physics-based simulation of blood flow tocompute patient-specific blood flow characteristics and clinicallyrelevant quantities of interest. Namely, the presently disclosed systemsand methods may incorporate machine learning techniques to predict theresults of a physics-based simulation. For example, the presentdisclosure describes an exemplary, less processing-intensive technique,which may involve modeling the fractional flow reserve (FFR) as afunction of a patient's vascular cross-sectional area, diseased length,and boundary conditions. The cross-sectional area may be calculatedbased on lumen segment and plaque segment, among other things. Thediseased length may be calculated based on plaque segment and stenosislocation, among other things. The boundary conditions may reflectpatient-specific physiology, such as coronary flow (estimated frommyocardial mass), outlet area, and hyperemic assumptions, to reflectthat different patients have different geometry and physiologicresponses.

In one embodiment, fractional flow reserve may be modeled as a functionof a patient's boundary conditions (f(BCs)), and a function of apatient's vascular geometry (g(areaReductions)). Although the patient'sgeometry may be described as a function of “areaReductions,” it shouldbe appreciated that this term refers, not just to changes in patient'svascular cross-sectional area, but to any physical or geometriccharacteristics affecting a patient's blood flow. In one embodiment, FFRcan be predicted by optimizing the functions “f” and “g” such that thedifference between the estimated FFR (FFR_(CT) _(_) _(ScalingLaw)) andthe measured FFR (mFFR) is minimized. In other words, machine learningtechniques can be used to solve for the functions that cause theestimated FFR to approximate the measured FFR. In one embodiment, themeasured FFR may be calculated by traditional catheterized methods or bymodern, computational fluid dynamics (CFD) techniques. In oneembodiment, one or more machine learning algorithms may be used tooptimize the functions of boundary conditions and patient geometry forhundreds or even thousands of patients, such that estimates for FFR canreliably approximate measured FFR values. Thus, FFR values calculated byCFD techniques can be valuable for training the machine learningalgorithms.

Referring now to the figures, FIG. 1 depicts a block diagram of anexemplary system and network for estimating patient-specific blood flowcharacteristics from vessel geometry and physiological information.Specifically, FIG. 1 depicts a plurality of physicians 102 and thirdparty providers 104, any of whom may be connected to an electronicnetwork 100, such as the Internet, through one or more computers,servers, and/or handheld mobile devices. Physicians 102 and/or thirdparty providers 104 may create or otherwise obtain images of one or morepatients' cardiac and/or vascular systems. The physicians 102 and/orthird party providers 104 may also obtain any combination ofpatient-specific information, such as age, medical history, bloodpressure, blood viscosity, etc. Physicians 102 and/or third partyproviders 104 may transmit the cardiac/vascular images and/orpatient-specific information to server systems 106 over the electronicnetwork 100. Server systems 106 may include storage devices for storingimages and data received from physicians 102 and/or third partyproviders 104. Sever systems 106 may also include processing devices forprocessing images and data stored in the storage devices.

FIG. 2 is a block diagram of an exemplary method for estimatingpatient-specific blood flow characteristics from vessel geometry andphysiological information, according to an exemplary embodiment of thepresent disclosure. The method of FIG. 2 may be performed by serversystems 106, based on information received from physicians 102 and/orthird party providers 104 over electronic network 100.

In one embodiment, the method of FIG. 2 may include a training method202, for training one or more machine learning algorithms based onnumerous patients' blood flow characteristic estimates, and a productionmethod 204 for using the machine learning algorithm results to predict aparticular patient's blood flow characteristics.

In one embodiment, training method 202 may be performed based on FFRestimates generating using CFD techniques for hundreds of patients.Training method 202 may involve acquiring, for each of a plurality ofindividuals, e.g., in digital format: (a) a patient-specific geometricmodel, (b) one or more measured or estimated physiological parameters,and (c) values of blood flow characteristics. Training method 202 maythen involve, for one or more points in each patient's model, creating afeature vector of the patients' physiological parameters and associatingthe feature vector with the values of blood flow characteristics. Forexample, training method 202 may associate an estimated FFR with everypoint in a patient's geometric model. Training method 202 may then traina machine learning algorithm (e.g., using processing devices of serversystems 106) to predict blood flow characteristics at each point of ageometric model, based on the feature vectors and blood flowcharacteristics. Training method 202 may then save the results of themachine learning algorithm, including feature weights, in a storagedevice of server systems 106. The stored feature weights may define theextent to which patient features or geometry are predictive of certainblood flow characteristics.

In one embodiment, the production method 204 may involve estimating FFRvalues for a particular patient, based on results of executing trainingmethod 202. In one embodiment, production method 204 may includeacquiring, e.g. in digital format: (a) a patient-specific geometricmodel, and (b) one or more measured or estimated physiologicalparameters. For multiple points in the patient's geometric model,production method 204 may involve creating a feature vector of thephysiological parameters used in the training mode. Production method204 may then use saved results of the machine learning algorithm toproduce estimates of the patient's blood flow characteristics for eachpoint in the patient-specific geometric model. Finally, productionmethod 204 may include saving the results of the machine learningalgorithm, including predicted blood flow characteristics, to a storagedevice of server systems 106.

Described below are general and specific exemplary embodiments forimplementing a training mode and a production mode of machine learningfor predicting patient-specific blood flow characteristics, e.g. usingserver systems 106 based on images and data received from physicians 102and/or third party providers 104 over electronic network 100.

General Embodiment

In a general embodiment, server systems 106 may perform a training modebased on images and data received from physicians 102 and/or third partyproviders 104 over electronic network 100. Specifically, for one or morepatients, server systems 106 may acquire a digital representation (e.g.,the memory or digital storage [e.g., hard drive, network drive] of acomputational device such as a computer, laptop, DSP, server, etc.) ofthe following items: (a) a patient-specific model of the geometry forone or more of the patient's blood vessels; (b) a list of one or moremeasured or estimated physiological or phenotypic parameters of thepatient; and/or (c) measurements, estimations or simulated values of allblood flow characteristic being targeted for prediction. In oneembodiment, the patient-specific model of the geometry may berepresented by a list of points in space (possibly with a list ofneighbors for each point) in which the space can be mapped to spatialunits between points (e.g., millimeters). In one embodiment, the list ofone or more measured or estimated physiological or phenotypic parametersof the patient may include blood pressure, blood viscosity, patient age,patient gender, mass of the supplied tissue, etc. These patient-specificparameters may be global (e.g., blood pressure) or local (e.g.,estimated density of the vessel wall at a particular location).

For every point in the patient-specific geometric model for which thereis a measured, estimated or simulated value of the blood flowcharacteristic, server systems 106 may then create a feature vector forthat point. The feature vector may be a numerical description of thepatient-specific geometry at that point and estimates of physiologicalor phenotypic parameters of the patient. The feature vector may containboth global and local physiological or phenotypic parameters, where: forglobal parameters, all points have the same numerical value; and forlocal parameters, the value(s) may change at different points in thefeature vector. Server systems 106 may then associate this featurevector with the measured, estimated or simulated value of the blood flowcharacteristic at this point.

Server systems 106 may then train a machine learning algorithm topredict the blood flow characteristics at the points from the featurevectors at the points. Examples of machine learning algorithms that canperform this task are support vector machines (SVMs), multi-layerperceptrons (MLPs), and multivariate regression (MVR) (e.g., weightedlinear or logistic regression). Server systems 106 may then save theresults of the machine learning algorithm (e.g., feature weights) to adigital representation (e.g., the memory or digital storage [e.g., harddrive, network drive] of a computational device such as a computer,laptop, DSP, server, etc.).

Also in a general embodiment, server systems 106 may perform aproduction mode based on images and data received from physicians 102and/or third party providers 104 over electronic network 100. For apatient on whom a blood flow analysis is to be performed, server systems106 may acquire a digital representation (e.g., the memory or digitalstorage [e.g., hard drive, network drive] of a computational device suchas a computer, laptop, DSP, server, etc.) of (a) a patient-specificmodel of the geometry for one or more of the patient's blood vessels;and (b) a list of one or more estimates of physiological or phenotypicparameters of the patient. In one embodiment, the patient-specific modelof the geometry for one or more of the patient's blood vessels may berepresented as a list of points in space (possibly with a list ofneighbors for each point) in which the space can be mapped to spatialunits between points (e.g., millimeters). The list of one or moreestimates of physiological or phenotypic parameters of the patient, mayinclude blood pressure, blood viscosity, patient age, patient gender,the mass of the supplied tissue, etc. These parameters may be global(e.g., blood pressure) or local (e.g., estimated density of the vesselwall at a location). This list of parameters must be the same as thelist used in the training mode.

For every point in the patient-specific geometric model, server systems106 may create a feature vector that consists of a numerical descriptionof the geometry and estimates of physiological or phenotypic parametersof the patient. Global physiological or phenotypic parameters can beused in the feature vector of all points and local physiological orphenotypic parameters can change in the feature vector of differentpoints. These feature vectors may represent the same parameters used inthe training mode. Server systems 106 may then use the saved results ofthe machine learning algorithm produced in the training mode (e.g.,feature weights) to produce estimates of the blood flow characteristicsat each point in the patient-specific geometric model. These estimatesmay be produced using the same machine learning algorithm technique usedin the training mode (e.g., the SVM, MLP, MVR technique). Server systems106 may also save the predicted blood flow characteristics for eachpoint to a digital representation (e.g., the memory or digital storage[e.g., hard drive, network drive] of a computational device such as acomputer, laptop, DSP, server, etc.).

Exemplary Embodiment

In one exemplary embodiment, server systems 106 may perform a trainingmode based on images and data received from physicians 102 and/or thirdparty providers 104 over electronic network 100. Specifically, for oneor more patients, server systems 106 may acquire a digitalrepresentation (e.g., the memory or digital storage [e.g., hard drive,network drive] of a computational device such as a computer, laptop,DSP, server, etc.) of (a) a patient-specific model of the geometry forthe patient's ascending aorta and coronary artery tree; (b) a list ofmeasured or estimated physiological or phenotypic parameters of thepatient; and (c) measurements of the FFR when available.

In one embodiment, the patient-specific model of the geometry for thepatient's ascending aorta and coronary artery tree may be represented asa list of points in space (possibly with a list of neighbors for eachpoint) in which the space can be mapped to spatial units between points(e.g., millimeters). This model may be derived by performing a cardiacCT imaging study of the patient during the end diastole phase of thecardiac cycle. The resulting CT images may then be segmented manually orautomatically to identify voxels belonging to the aorta and to the lumenof the coronary arteries. Once all relevant voxels are identified, thegeometric model can be derived (e.g., using marching cubes).

In one embodiment, the list of measured or estimated physiological orphenotypic parameters of the patient may be obtained and may include:(i) systolic and diastolic blood pressures; (ii) heart rate; (iii)hematocrit level; (iv) patient age, gender, height, weight, generalhealth status (presence or absence of diabetes, current medications);(v) lifestyle characteristics: smoker/non-smoker; and/or (vi) myocardialmass (may be derived by segmenting the myocardium obtained during the CTimaging study and then calculating the volume in the image; the mass isthen computed using the computed volume and an estimated density (1.05g/mL) of the myocardial mass.

In one embodiment, measurements of the FFR may be obtained whenavailable. If the measured FFR value is not available at a given spatiallocation in the patient-specific geometric model, then a numericallycomputed value of the FFR at the point may be used. The numericallycomputed values may be obtained from a previous CFD simulation using thesame geometric model and patient-specific boundary conditions derivedfrom the physiological and phenotypic parameters listed above.

For every point in the patient-specific geometric model for which thereis a measured, estimated or simulated value of the blood flowcharacteristics, server systems 106 may create a feature vector for thatpoint that contains a numerical description of physiological orphenotypic parameters of the patient and a description of the localgeometry. Specifically the feature vector may contain: (i) systolic anddiastolic blood pressures; (ii) heart rate; (iii) blood propertiesincluding: plasma, red blood cells (erythrocytes), hematocrit, whiteblood cells (leukocytes) and platelets (thrombocytes), viscosity, yieldstress; (iv) patient age, gender, height, weight, etc.; (v) diseases:presence or absence of diabetes, myocardial infarction, malignant andrheumatic conditions, peripheral vascular conditions, etc.; (vi)lifestyle characteristics: presence or absence of currentmedications/drugs, smoker/non-smoker; (vii) characteristics of theaortic geometry (Cross-sectional area of the aortic inlet and outlet,Surface area and volume of the aorta, Minimum, maximum, and averagecross-sectional area, etc.); (viii) characteristics of the coronarybranch geometry; and (ix) one or more feature sets.

In one embodiment, the characteristics of the coronary branch geometrymay include: (i) volumes of the aorta upstream/downstream of thecoronary branch point; (ii) cross-sectional area of the coronary/aortabifurcation point, i.e., inlet to the coronary branch; (iii) totalnumber of vessel bifurcations, and the number of upstream/downstreamvessel bifurcations; (iv) average, minimum, and maximumupstream/downstream cross-sectional areas; (v) distances (along thevessel centerline) to the centerline point of minimum and maximumupstream/downstream cross-sectional areas; (vi) cross-sectional of anddistance (along the vessel centerline) to the nearestupstream/downstream vessel bifurcation; (vii) cross-sectional area ofand distance (along the vessel centerline) to the nearest coronaryoutlet and aortic inlet/outlet; (viii) cross-sectional areas anddistances (along the vessel centerline) to the downstream coronaryoutlets with the smallest/largest cross-sectional areas; (ix)upstream/downstream volumes of the coronary vessels; and (x)upstream/downstream volume fractions of the coronary vessel with across-sectional area below a user-specified tolerance.

In one embodiment, a first feature set may define cross-sectional areafeatures, such as a cross-sectional lumen area along the coronarycenterline, a powered cross-sectional lumen area, a ratio of lumencross-sectional area with respect to the main ostia (LM, RCA), a poweredratio of lumen cross-sectional area with respect to the main ostia, adegree of tapering in cross-sectional lumen area along the centerline,locations of stenotic lesions, lengths of stenotic lesions, location andnumber of lesions corresponding to 50%, 75%, 90% area reduction,distance from stenotic lesion to the main ostia, and/or irregularity (orcircularity) of cross-sectional lumen boundary.

In one embodiment, the cross-sectional lumen area along the coronarycenterline may be calculated by extracting a centerline from constructedgeometry, smoothing the centerline if necessary, and computingcross-sectional area at each centerline point and map it tocorresponding surface and volume mesh points. In one embodiment, thepowered cross-sectional lumen area can be determined from various sourceof scaling laws. In one embodiment, the ratio of lumen cross-sectionalarea with respect to the main ostia (LM, RCA) can be calculated bymeasuring cross-sectional area at the LM ostium, normalizingcross-sectional area of the left coronary by LM ostium area, measuringcross-sectional area at the RCA ostium, and normalizing cross-sectionalarea of the right coronary by RCA ostium area. In one embodiment, thepowered ratio of lumen cross-sectional area with respect to the mainostia can be determined from various source of scaling laws. In oneembodiment, the degree of tapering in cross-sectional lumen area alongthe centerline can be calculated by sampling centerline points within acertain interval (e.g., twice the diameter of the vessel) and compute aslope of linearly-fitted cross-sectional area. In one embodiment, thelocation of stenotic lesions can be calculated by detecting minima ofcross-sectional area curve, detecting locations where first derivativeof area curve is zero and second derivative is positive, and computingdistance (parametric arc length of centerline) from the main ostium. Inone embodiment, the lengths of stenotic lesions can be calculated bycomputing the proximal and distal locations from the stenotic lesion,where cross-sectional area is recovered.

In one embodiment, another feature set may include intensity featuresthat define, for example, intensity change along the centerline (slopeof linearly-fitted intensity variation). In one embodiment, anotherfeature set may include surface features that define, for example, 3Dsurface curvature of geometry (Gaussian, maximum, minimum, mean). In oneembodiment, another feature set may include volume features that define,for example, a ratio of total coronary volume compared to myocardialvolume. In one embodiment, another feature set may include centerlinefeatures that define, for example, curvature (bending) of coronarycenterline, e.g., by computing Frenet curvature:

${\kappa = \frac{{p^{\prime} \times p^{''}}}{{p^{\prime}}^{3}}},$

where p is coordinate of centerline

or by computing an inverse of the radius of circumscribed circle alongthe centerline points. Curvature (bending) of coronary centerline mayalso be calculated based on tortuosity (non-planarity) of coronarycenterline, e.g., by computing Frenet torsion:

${\tau = \frac{( {p^{\prime} \times p^{''}} ) \cdot p^{\prime\prime\prime}}{{{p^{\prime} \times p^{''}}}^{2}}},$

where p is coordinate of centerline

In one embodiment, another feature set may include a SYNTAX scoringfeature, including, for example, an existence of aorto ostial lesion,detection of a lesion located at the origin of the coronary from theaorta; and/or dominance (left or right).

In one embodiment, another feature set may include a simplified physicsfeature, e.g., including a fractional flow reserve value derived fromHagen-Poisseille flow assumption (Resistance˜Area⁻²). For example, inone embodiment, server systems 106 may compute the cross-sectional areaof the origin (LM ostium or RCA ostium) of the coronary from the aorta(A₀) with aortic pressure (P₀); compute cross-sectional area of coronaryvessel (A_(i)) at each sampled interval (L_(i)); determine the amount ofcoronary flow in each segment of vessel using resistance boundarycondition under hyperemic assumption (Q_(i)); estimate resistance ateach sampled location (R_(i)) based on:

${R_{i} = {{\alpha_{i}\frac{8\mu \; L_{i}}{\pi \; A_{i}^{\gamma_{i}}}} + \beta_{i}}},$

where:

Nominal value μ=dynamic viscosity of blood, α_(i)=1.0, β_(i)=0,γ_(i)=2.0 (Hagen-Poisseille).

Server systems 106 may estimate pressure drop (ΔP_(i)) asΔP_(i)=Q_(i)R_(i) and compute FFR at each sampled location as

${FFR}_{i} = {\frac{P_{0} - {\sum_{k = 1}^{i}{\Delta \; P_{k}}}}{P_{0}}.}$

Locations of cross-sectional area minima or intervals smaller thanvessel radius may be used for sampling locations. Server systems 106 mayinterpolate FFR along the centerline using FFR_(i), project FFR valuesto 3D surface mesh node, and vary α_(i), β_(i), γ_(i) and obtain newsets of FFR estimation as necessary for training, such as by using thefeature sets defined above to perturb parameters where α_(i), β_(i) canbe a function of the diseased length, degree of stenosis and taperingratio to account for tapered vessel; and Q_(i) can be determined bysumming distributed flow of each outlet on the basis of the same scalinglaw as the resistance boundary condition (outlet resistance∝outletarea^(−1.35)). However, a new scaling law and hyperemic assumption canbe adopted, and this feature vector may be associated with themeasurement or simulated value of the FFR at that point. Server systems106 may also train a linear SVM to predict the blood flowcharacteristics at the points from the feature vectors at the points;and save the results of the SVM as a digital representation (e.g., thememory or digital storage [e.g., hard drive, network drive] of acomputational device such as a computer, laptop, DSP, server, etc.).

In an exemplary production mode, servers systems 106 may, for a targetpatient, acquire in digital representation (e.g., the memory or digitalstorage (e.g., hard drive, network drive) of a computational device suchas a computer, laptop, DSP, server, etc.): (a) a patient-specific modelof the geometry for the patient's ascending aorta and coronary arterytree; and (b) a list of physiological and phenotypic parameters of thepatient obtained during training mode. In one embodiment, thepatient-specific model of the geometry for the patient's ascending aortaand coronary artery tree may be represented as a list of points in space(possibly with a list of neighbors for each point) in which the spacecan be mapped to spatial units between points (e.g., millimeters). Thismodel may be derived by performing a cardiac CT imaging of the patientin the end diastole phase of the cardiac cycle. This image then may besegmented manually or automatically to identify voxels belonging to theaorta and the lumen of the coronary arteries. Once the voxels areidentified, the geometric model can be derived (e.g., using marchingcubes). The process for generating the patient-specific model of thegeometry may be the same as in the training mode. For every point in thepatient-specific geometric model, the server systems 106 may create afeature vector for that point that consists of a numerical descriptionof the geometry at that point and estimates of physiological orphenotypic parameters of the patient. These features may be the same asthe quantities used in the training mode. The server systems 106 maythen use the saved results of the machine learning algorithm produced inthe training mode (e.g., feature weights) to produce estimates of theFFR at each point in the patient-specific geometric model. Theseestimates may be produced using the same linear SVM technique used inthe training mode. The server systems 106 may save the predicted FFRvalues for each point to a digital representation (e.g., the memory ordigital storage [e.g., hard drive, network drive] of a computationaldevice such as a computer, laptop, DSP, server, etc.).

In one embodiment, the above factors (i) thru (viii) (“Systolic anddiastolic blood pressures” thru “Characteristics of the coronary branchgeometry”) may be considered global features, which are applicable toall points within a given patient's geometric model. Also, items (ix)thru (xv) (“Feature Set I: Cross-sectional area feature” thru “FeatureSet VII: Simplified Physics feature”) may be considered features thatare local to specific points within a given patient's geometric model.In addition, features (i) thru (vi) may be considered variables withinthe function of boundary conditions, f(BCs), while features (vii) thru(xv) may be considered variables within the function of geometry,g(areaReductions), on that page. It will be appreciated that anycombination of those features, modified by any desired weighting scheme,may be incorporated into a machine learning algorithm executed accordingto the disclosed embodiments.

In another embodiment, systems and methods are described to obtainestimates of physiologic metrics, such as ischemia, blood flow, or FFRfrom patient-specific anatomy and characteristics. The system mayconsist of a computer and software either on-site at a hospital oroff-site that physicians load or transfer patient-specific data to. Theanatomic data may consist of imaging data (ie CT) or measurements andanatomic representation already obtained from imaging data (quantitativeangiography, vessel segmentations from third party software, vasculardiameters, etc). Other patient characteristics may consist of heartrate, blood pressure, demographics such as age or sex, medication,disease states including diabetes and hypertension, prior MI, etc.

After relevant data is received by the system, it may be processed bysoftware automation, the physician using the system, a third-partytechnician or analyst using the system, or any combination. The data maybe processed using algorithms relating the patient's anatomy andcharacteristics to functional estimates of ischemia and blood flow. Thealgorithms may employ empirically derived models, machine learning, oranalytical models relating blood flow to anatomy. Estimates of ischemia(blood flow, FFR, etc) may be generated for a specific location in avessel, as an overall estimate for the vessel, or for an entire systemof vessels such as the coronary arteries. A numeric output, such as anFFR value, may be generated or simple positive/negative/inconclusiveindications based on clinical metrics may be provided (ie FFR > or<0.80). Along with the output, a confidence may be provided. Results ofthe analysis may be displayed or stored in a variety of media, includingimages, renderings, tables of values, or reports and may be transferredback to the physician through the system or through other electronic orphysical delivery methods.

In one embodiment, the algorithm to estimate FFR from patient anatomyconsists of deriving an analytical model based on fundamentals ofphysiology and physics, for example analytical fluid dynamics equationsand morphometry scaling laws. Information about the following coronaryanatomy, including but not limited to the following features derivedfrom imaging data (ie CT), serves as an input:

Vessel sizes

Vessel size at ostium

Vessel size at distal branches

Reference and minimum vessel size at plaque

Distance from ostium to plaque

Length of plaque and length of minimum vessel size

Myocardial volume

Branches proximal/distal to measurement location

Branches proximal/distal to plaque

Measurement location

Using some or all of the information above, a network of flow resistancemay be created. Pressure drop may be estimated by relating the amount ofblood flow to the resistance to blood flow using any of a variety ofanalytical models, such as Poiseuille's equation, energy loss models,etc. As an example embodiment:

FFR=(P−ΔP)/P

where P is the aortic pressure and ΔP is the change in pressure from theaorta to the location of interest.

ΔP=QR,

where Q is flow rate, and R is resistance

The flow rate may be estimated by morphometry relations, such as Q∝M^(k)where M is the myocardial volume and k is an exponent, oftenapproximately 0.75. Individual vessel flow rates may scale based on themorphometry relationship of Q∝D^(k) where D is the diameter of thevessel and k is an exponent, often between 2 and 3.

In an example embodiment, the resistance through a vessel may beestimated by Poiseuille's equation:

R∝μL/D ⁴

where u is viscosity, L is length, and D is diameter

Downstream, or microvascular resistances may be estimated throughmorphometric tree generation or other methods described in Ser. No.13/014,809 and Ser. No. 8/157,742. FFR can be estimated by relating allthe resistance and flow estimates in a network representing thedistribution of vessels in the coronary circulation, and pressure can besolved.

In another embodiment, regression or machine learning may be employed totrain the algorithm using the features previously mentioned,formulations of resistances and flows, and additional anatomic andpatient characteristics, including but not limited to:

Age, sex, and other demographics

Heart rate, blood pressure, and other physiologic measures

Disease state, such as hypertension, diabetes, previous cardiac events

Vessel dominance

Plaque type

Plaque shape

Prior simulation results, such as full 3D simulations of FFR

A library or database of anatomic and patient characteristics along withFFR, ischemia test results, previous simulation results, imaging data,or other metrics may be compiled. For every point of interest where anFFR estimation is required, a set of features may be generated. Aregression or machine learning technique, such as linear regression ordecision trees, may be used to define which features have the largestimpact on estimating FFR and to create an algorithm that weights thevarious features. Example embodiments may estimate FFR numerically,classify a vessel as ischemia positive or negative, or classify apatient as ischemia positive or negative.

Once an algorithm is created, it may be executed on new data provided bythe physician to the system. As previously described, a number ofmethods may be used to generate the anatomic information required, andonce obtained, the features defined, algorithm performed, and resultsreported. Along with numerical or classification results, a confidencefrom the machine learning algorithm may be provided. One exampleembodiment is to report that a particular vessel in a patient has aspecific percent confidence of being positive or negative for ischemia,ie Left anterior descending artery is positive with 85% confidence. Overtime, the algorithm may be refined or updated as additional patient datais added to the library or database.

One additional embodiment is to derive any of the previously mentionedparameters, physiologic, or physical estimations empirically. Coupledwith machine learning or analytic techniques, empirical studies of flowand pressure across various geometries may be utilized to inform thealgorithms.

Other embodiments of the invention will be apparent to those skilled inthe art from consideration of the specification and practice of theinvention disclosed herein. It is intended that the specification andexamples be considered as exemplary only, with a true scope and spiritof the invention being indicated by the following claims.

1. A method for determining individual-specific blood flowcharacteristics, the method comprising: acquiring, for each of aplurality of individuals, individual-specific anatomic data and bloodflow characteristics of at least part of the individual's vascularsystem; executing a machine learning algorithm on theindividual-specific anatomic data and blood flow characteristics foreach of the plurality of individuals; relating, based on the executedmachine learning algorithm, each individual's individual-specificanatomic data to functional estimates of blood flow characteristics;acquiring, for an individual, individual-specific anatomic data of atleast part of the individual's vascular system; and for at least onepoint in the individual's individual-specific anatomic data, determininga blood flow characteristic of the individual, using relations from thestep of relating individual-specific anatomic data to functionalestimates of blood flow characteristics.
 2. The method of claim 1,further comprising: acquiring, for each of the plurality of individuals,one or more individual characteristics; and executing the machinelearning algorithm further based on the one or more individualcharacteristics.
 3. The method of claim 1, wherein the blood flowcharacteristics of the individuals include ischemia, blood flow, orfractional flow reserve.
 4. The method of claim 1, further comprising:generating a set of features for each point of interest where a bloodflow characteristic is desired; using a regression or machine learningtechnique to weight the impact of features on the blood flowcharacteristic; and using the regression or machine learning techniqueto estimate a blood flow characteristic numerically, classify a vesselas ischemia positive or negative, or classify an individual as ischemiapositive or negative.
 5. The method of claim 2, wherein the individualcharacteristics include one or more of: heart rate, blood pressure,demographics such as age or sex, medication, disease states, includingdiabetes, hypertension, vessel dominance, and prior MI.
 6. The method ofclaim 1, further comprising: displaying or storing the producedestimates in one or more of a media, including images, renderings,tables of values, or reports, or transferring the produced estimates toa physician through other electronic or physical delivery methods. 7.The method of claim 1, further comprising displaying along with eachproduced estimate a confidence level or a positive, negative, orinconclusive indication.
 8. The method of claim 1, further comprisingproducing estimates based on one or more of analytical fluid dynamicsequations and morphometry scaling laws.
 9. The method of claim 1,wherein the individual-specific anatomic data includes one or more of:vessel size, vessel size at ostium, vessel size at distal branches,reference and minimum vessel size at plaque, distance from ostium toplaque, length of plaque and length of minimum vessel size, myocardialvolume, branches proximal/distal to measurement location, branchesproximal/distal to plaque, and measurement location.
 10. The method ofclaim 2, further comprising: compiling a library or database of anatomicand individual characteristics along with FFR, ischemia test results,previous simulation results, and imaging data.
 11. The method of claim10, further comprising: refining the machine learning algorithm based onadditional data added to the library or database.
 12. The method ofclaim 10, wherein the individual-specific anatomic data for theindividual or the plurality of individuals is obtained from one or moreof: medical image data, measurements, models, and segmentations.
 13. Asystem for determining individual-specific blood flow characteristics,the system comprising: a data storage device storing instructions forestimating individual-specific blood flow characteristics; and aprocessor configured to execute the instructions to perform a methodincluding the steps of: acquiring, for each of a plurality ofindividuals, individual-specific anatomic data and blood flowcharacteristics of at least part of the individual's vascular system;executing a machine learning algorithm on the individual-specificanatomic data and blood flow characteristics for each of the pluralityof individuals; relating, based on the executed machine learningalgorithm, each individual's individual-specific anatomic data tofunctional estimates of blood flow characteristics; acquiring, for anindividual, individual-specific anatomic data of at least part of theindividual's vascular system; and for at least one point in theindividual's individual-specific anatomic data, determining a blood flowcharacteristic of the individual, using relations from the step ofrelating individual-specific anatomic data to functional estimates ofblood flow characteristics.
 14. The system of claim 13, wherein thesystem is further configured for: acquiring, for each of the pluralityof individuals, one or more individual characteristics; and executingthe machine learning algorithm further based on the one or moreindividual characteristics.
 15. The system of claim 13, wherein theblood flow characteristics include ischemia, blood flow, or fractionalflow reserve.
 16. The system of claim 13, wherein the processor isfurther configured for: generating a set of features for each point ofinterest where a blood flow characteristic is desired; using aregression or machine learning technique to weight the impact offeatures on estimated blood flow characteristic; and using theregression or machine learning technique to estimate a blood flowcharacteristic numerically, classify a vessel as ischemia positive ornegative, or classify an individual as ischemia positive or negative.17. The system of claim 14, wherein the individual characteristicsinclude one or more of: heart rate, blood pressure, demographics such asage or sex, medication, disease states, including diabetes,hypertension, vessel dominance, and prior MI.
 18. The system of claim13, wherein the processor is further configured for: displaying orstoring the produced estimates in one or more of a media, includingimages, renderings, tables of values, or reports, or transferring theproduced estimates to a physician through other electronic or physicaldelivery methods.
 19. The system of claim 13, wherein the processor isfurther configured for: displaying along with each produced estimate aconfidence level or a positive, negative, or inconclusive indication.20. The system of claim 13, further comprising producing estimates basedon one or more of analytical fluid dynamics equations and morphometryscaling laws.